arXiv subjects

Emile Meoto

Publications and source records attributed to Emile Meoto.

8 recordsLinked to original sources

arXiv2026

Raubold-Lynch construction of the phase space in hypertriton three-body mesonic decay

A Monte Carlo construction is presented for the three-body mesonic decay phase space of the hypertriton. This is accomplished using the Raubold-Lynch sequential two-body decay algorithm. The method factorises this three-body decay into successive two-body decays through a virtual intermediate subsystem, whose invariant mass is sampled over the full kinematically allowed region. Exact relativistic two-body kinematics and Lorentz transformations are employed to construct complete four-momenta for all decay products. The construction is applied to both charged- and neutral-pion decay channels, yielding events that reproduce the Lorentz-invariant three-body phase-space measure. The resulting momentum spectra, pairwise momentum correlations, opening-angle distributions, and Dalitz plots furnish a complete kinematic characterisation of both decay modes. The neutral-pion channel exhibits a larger available three-body energy and correspondingly broader kinematic limits. The unweighted events generated provide a kinematic baseline that can subsequently be weighted event by event with a weak-decay matrix element, for computing decay rates and other observables. For the neutral-pion channel, where no experimental data currently exists, the Lorentz-invariant phase-space constitutes a useful baseline for predictions.

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arXiv2026

Neutral pion momentum in hypertriton mesonic decay through a root-finding method

A root-finding method is used to study two-body mesonic decay in the hypertriton. We validate this Newton--Raphson root-finding approach by applying it to the negative-pion decay channel ($^{3}_{\Lambda}\mathrm{H} \rightarrow {}^{3}\mathrm{He} + \pi^{-}$), for which the pion momentum and lambda binding energy were recently reported by MAMI A1 Collaboration as $p_{\pi^-} = 113.789 \pm 0.020_{\text{stat.}} \pm 0.112_{\text{syst.}} \text{ MeV}/c$ and $B_{\Lambda} = 0.523 \pm 0.013_{\text{stat.}} \pm 0.075_{\text{syst.}}$ MeV, respectively. Using their reported $\Lambda$ binding energy, the root-finding method and an exact kinematic formula both yield $p_{\pi^{-}} = 113.790$ MeV/$c$, agreeing with each other. We then apply both the Newton--Raphson method and the exact formula to the neutral-pion decay channel ($^{3}_{\Lambda}\mathrm{H} \rightarrow {}^{3}\mathrm{H} + \pi^{0}$), for which the neutral pion momentum cannot be directly measured due to difficulties in experimental setup. Both methods agree, yielding a predicted neutral-pion momentum of $p_{\pi^{0}} = 118.129$ MeV/$c$. This validates the root-finding algorithm as a robust equivalent for predicting pion momenta that may be experimentally inaccessible in some cases. Furthermore, it establishes the method as a reliable tool for extension to three-body mesonic decays, for which the pion momentum is a continuum and the exact kinematic formula can no longer be applied. In addition, the pion momentum computed allows for its 4-momentum to be completely determined, a useful input for investigating its two-photon decay ($\pi^0 \to \gamma \gamma$) in the rest frame of the hypertriton.

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arXiv2026

4-momentum conservation as the principal framework for mesonic decay: The case of helium-5-lambda

Negative-pion and neutral-pion mesonic decays of the hypernucleus $ _\Lambda ^5$He are investigated within two-body and three-body relativistic kinematics in the rest-frame of the hypernucleus. 4-momentum conservation fully constrains the two-body decay, giving rise to a monochromatic pion momentum that is determined through the Newton-Raphson root-finding algorithm. In the case of three-body decay, where 4-momentum conservation is insufficient, the final-state momenta are parametrised by variables whose variations account for all kinematically allowed momenta. A Monte Carlo sampling method is then employed to generate 50 000 decay events per channel that simultaneously satisfy both energy and momentum conservation. The resulting pion momentum distributions exhibit clear peaks at 103.0 MeV/c for neutral pion decay and 97.3 MeV/c for negative pion decay. In addition, only 0.27\% of neutral pion decay events and 0.03\% of negative pion decay events produce nucleons with momenta exceeding the Fermi momentum of $ ^4$He, and are therefore allowed by the Pauli exclusion principle.

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arXiv2026

Explicit asymptotics of coupling matrix elements for central potentials in the hyperspherical harmonics expansion method

The analytic structure and asymptotic behavior of channel-coupling potentials in three-body systems are investigated within the framework of the hyperspherical harmonics expansion method. The coupling between different Jacobi partitions is expressed using Raynal--Revai transformation coefficients and a reduced hyperangular integral that contains the two-body interaction. For central potentials, this integral is factorised into geometric and dynamical components. Explicit asymptotic scaling laws are derived for the hyperradial coupling strength in the limit of large hyperradius $\rho \to \infty$ for representative nuclear potentials: Gaussian, Yukawa, and Woods--Saxon potentials (short-range), and Coulomb potential (long-range). These short-range potentials are found to exhibit an algebraic decay $\propto \rho^{-(2\ell_{\eta_i}+3)}$, where $\ell_{\eta_i}$ is the orbital angular momentum of the interacting pair. This decay is shown to lead to efficient asymptotic decoupling of hyperspherical channels. In contrast, the Coulomb interaction yields couplings that decay only as $1/\rho$, indicating persistent channel coupling at large distances and explaining the slow convergence of hyperspherical expansions for charged systems. These results provide a quantitative basis for truncating the hyperradial domain, for example, in choosing a matching radius for scattering calculations or an upper integration limit in bound-state problems.

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arXiv2025

Quantum three-body problem for nuclear physics

A brief excursion into the three-body problem in quantum mechanics is presented for graduate students or researchers in nuclear physics. Starting from single-particle coordinates, the three-body Schr\"{o}dinger equation is systematically transformed into a representation in Jacobi coordinates. Gradient, Laplacian, and kinetic energy operators are explicitly derived using the multivariable chain rule. Faddeev equations are reformulated in hyperspherical coordinates. In all transformations (from single-particle coordinates to Jacobi coordinates, rotation between Jacobi coordinates and from Jacobi coordinates to hyperspherical coordinates) the determinant of the Jacobian matrix is computed to ensure correct transformation of volume elements. The Faddeev equations in hyperspherical coordinates are projected onto a hyperspherical harmonics basis, leading to the coupled hyperradial equations that define the hyperspherical harmonics method.

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arXiv2020

Hypertriton states from inverse scattering theory

The primary goal of this paper is to demonstrate that inverse scattering theory is a viable method for the simulation of lambda-nucleon potentials in hypernuclear few-body studies. To this end, we investigate the hypertriton, modelled as a $\Lambda np$ three-body system in the $J^\pi = 1/2^+$ and $3/2^+$ channels. This three-body problem is solved using a hyperspherical-harmonic expansion of the Faddeev equations. The $\Lambda p$ and $\Lambda n$ interactions are modelled by the GLM-YN0 potentials. These simulated potentials were recovered through Gel'fand--Levitan--Marchenko inverse scattering theory as phase-equivalent simulations of the NSC97f meson-exchange model. The neutron-proton interaction is described by the semi-realistic Malfliet--Tjon I/III potential, with both singlet and triplet channels retained. For the ground state ($J^\pi = 1/2^+$), we obtain a binding energy of $-2.335$~MeV, corresponding to a $\Lambda$ separation energy of $B_\Lambda = +0.104$~MeV relative to the $\Lambda + d$ breakup threshold. This value is comparable to those from lambda-nucleon potentials that are simulated through G-matrix methods. The excited $J^\pi = 3/2^+$ state is found to have a lambda separation energy of $B_{\Lambda}=-1.444 $~MeV relative to the $\Lambda + d$ breakup threshold, confirming that there is no bound excited hypertriton state.

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arXiv2020

Faddeev calculations on lambda hypertriton with potentials from Gel'fand-Levitan-Marchenko theory

Effective lambda-proton and lambda-neutron potentials, restored from theoretical scattering phases through Gel'fand-Levitan-Marchenko theory, are tested on a lambda hypertriton through three-body calculations. The lambda hypertriton is treated as a three-body system consisting of lambda-proton, lambda-neutron and proton-neutron subsystems. Binding energy and root-mean-square radius are computed for the ground state of lambda hypertriton ($J^π=1/2^+$). In coordinate space, the dynamics of the system is described using a set of coupled hyperradial equations obtained from the Differential Faddeev Equations. By solving the eigenvalue problem derived from this set of coupled hyperradial equations, the binding energy and root-mean-square matter radius computed are found to be -2.462 MeV and 7.00 fm, respectively. The potentials are also shown to display a satisfactory convergence behaviour.

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arXiv2019

Effective lambda-proton and lambda-neutron potentials from subthreshold inverse scattering

Potentials are constructed for the lambda-nucleon interaction in the $^1\text{S}_0$ and $^3\text{S}_1$ channels. These potentials are recovered from scattering phases below the inelastic threshold through Gel'fand-Levitan-Marchenko theory. Experimental data with good statistics is not available for lambda-nucleon scattering. This leaves theoretical scattering phases as the only option through which the rigorous theory of quantum inverse scattering can be used in probing the lambda-nucleon force. Using rational-function interpolations on the theoretical scattering data, the kernels of the Gel'fand-Levitan-Marchenko integral equation become degenerate, resulting in a closed-form solution. The new potentials restored, which are shown to be unique through the Levinson theorem, bear the expected features of short-range repulsion and intermediate-range attraction. Charge symmetry breaking, which is perceptible in the scattering phases, is preserved in the new potentials. The lambda-nucleon force in the $^1\text{S}_0$ channel is observed to be stronger than in the $^3\text{S}_1$ channel, as expected. In addition, the potentials bear certain distinctive features whose effects on hypernuclear systems can be explored through Schrödinger calculations.

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